Question

12. Scrieti sub forma de intervale multimile: a) A = {x apartine R | $\sqrt{(2x+3)^{2} } \leq 9$}

b) A = {x apartine R | $\sqrt{(2x-7)^{2}} \ \textless \ 3 }$}


DAU COROANAA !!!

Answer 1

Explicație pas cu pas:

$\sqrt{(2x+3)^{2} } \leq 9$

$|2x + 3| \leqslant 9 \iff - 9 \leqslant 2x + 3 \leqslant 9$

$- 12 \leqslant 2x \leqslant 6 \implies - 6 \leqslant x \leqslant 3$

=> A = [-6; 3]

$\sqrt{(2x-7)^{2}} < 3$

$|2x - 7| < 3 \iff - 3 < 2x - 7 < 3$

$4 < 2x < 10 \implies 2 < x < 5$

=> A = (2; 5)

Answer 2

$\it a)\ \ \sqrt{(2x+3)^2}\leq9 \Rightarrow |2x+3|\leq9 \Rightarrow -9\leq2x+3\leq9|_{-3}\ \Rightarrow \\ \\ \Rightarrow -12\leq2x\leq 6|_{:2} \Rightarrow -6\leq x\leq 3 \Rightarrow A=[-6,\ 3]$